Wanting a single phase motor is an odd priority for choosing a machine tool. Is it because 'old ways are best'? If so, it doesn't apply to single-phase motors!
Getting an electric motor to run on single-phase AC is quite difficult, and the way it's done is always a compromise. The advantage is a motor that runs off ordinary domestic electricity, but they come with many disadvantages: unreliable due to capacitors, centrifugal switches, and delicate start windings, relatively inefficient, they vibrate, and don't like being continually stopped and restarted. In short, a poor choice for a machine tool, unless the workshop only had single-phase power.
DC and 3-phase motors both outperform single-phase types but back in the day, it was expensive to convert single-phase power into DC or 3-phase. Today's electronics can do either at reasonable cost and it's unusual to find new machine tools fitted with single-phase motors. Likewise, many faced with replacing a failed single-phased motor on a old machine, choose to replace single-phase with 3-phase powered by a VFD, which provides speed control, low vibration and other significant benefits.
Another point, of all the parts on an elderly tool likely to need replacing the motor is usually, not always, the easiest. Standardised mountings have been used for years so there's a good chance a new one will just drop in. Not so the rest of the machine: bearings and other spares might be difficult to source, while wear and tear can require significant remedial work – time and money. So I'd prioritise the machine's mechanical condition above all else. The motor is bottom of the list, except watch out for machines with special motors and complicated drive arrangements designed to provide variable speed; they can be difficult to replace, rewire, and worn mechanical parts may be unobtainable or cost more than the whole machine.
Not that many different older small milling machines available. Tom Senior seem more common than Centecs, and jig borers turn up from time to time. Industry and education seem to have preferred bigger machines, especially Bridgeports, and horizontals. Mill-drilling machines of the hobby-type are a more recent arrival, and a good thing too, because they provide a choice of size from table-top to big workshop via modest shed.
Dave